Abstract:
The Geometric Boundary Theorem addresses the case in which a cofiber sequence induces a short exact sequence in cohomology. More generally, the factorization of the long exact sequence in cohomology into the composite of a short exact sequence and a 2-extension gives information about the Adams $d_2$ differential in terms of Yoneda composite with the 2-extension. This allows determination of the $E_3$ and $E_\infty$ terms in several cases of interest, including the connective image-of-J spectrum, its mod 2 reduction, the fiber of $Sq^n$ and the Tate normal spectrum $L^{tn}(Z)$.